Clustering by Orthogonal Non-negative Matrix Factorization: A Sequential Non-convex Penalty Approach

Shuai Wang, Tsung Hui Chang, Ying Cui, Jong Shi Pang

Research output: Chapter in Book/Report/Conference proceedingConference contribution

12 Scopus citations

Abstract

The non-negative matrix factorization (NMF) model with an additional orthogonality constraint on one of the factor matrices, called the orthogonal NMF (ONMF), has been found to provide improved clustering performance over the K-means. The ONMF model is a challenging optimization problem due to the orthogonality constraint, and most of the existing methods directly deal with the constraint in its original form via various optimization techniques. In this paper, we propose an equivalent problem reformulation that transforms the orthogonality constraint into a set of norm-based non-convex equality constraints. We then apply a penalty approach to handle these non-convex constraints. The penalized formulation is smooth and has convex constraints, which is amenable to efficient computation. We analytically show that the penalized formulation will provide a feasible stationary point of the reformulated ONMF problem when the penalty is large. Numerical results show that the proposed method greatly outperforms the existing methods.

Original languageEnglish (US)
Title of host publication2019 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2019 - Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages5576-5580
Number of pages5
ISBN (Electronic)9781479981311
DOIs
StatePublished - May 2019
Externally publishedYes
Event44th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2019 - Brighton, United Kingdom
Duration: May 12 2019May 17 2019

Publication series

NameICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
Volume2019-May
ISSN (Print)1520-6149

Conference

Conference44th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2019
Country/TerritoryUnited Kingdom
CityBrighton
Period5/12/195/17/19

Bibliographical note

Funding Information:
The work is supported by the NSFC, China, under Grant 61571385 and 61731018, and by the Shenzhen Fundamental Research Fund under Grant ZDSYS201707251409055 and KQTD2015033114415450.

Publisher Copyright:
© 2019 IEEE.

Keywords

  • Clustering
  • orthogonal NMF
  • penalty method

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